In a right-angled triangle ABC, leg BC and hypotenuse AB are 12 cm and 13 cm, respectively.

In a right-angled triangle ABC, leg BC and hypotenuse AB are 12 cm and 13 cm, respectively. Find sin B, cos B, tan B, ctg B.

Through the length of the hypotenuse AB and the adjacent leg BC, we determine the cosine of the angle ABC.

CosABC = BC / AB = 12/13.

We define the sine of the same angle through the cosine of the angle.

Sin2ABC = 1 – Cos2ABC = 1 – (12/13) ^ 2 = 1 – 144/169 = 25/169.

SinABC = 5/13.

Then tgABC = SinABC / CosABC = (5/13) / (12/13) = 5/12.

CtgABC = 1 / tgABC = 1 / (5/12) = 12/5.

Answer: SinABC = 5/13, CosABC = 12/13, tgABC = 5/12, ctgABC = 12/5.